\subsection*{实验1.三棱镜顶角的测量}
\subsubsection*{(1)原始数据记录表格}

\begin{center}

\begin{tabular}{|c|c|c|c|c|c|}
\hline 
i & 1 & 2 & 3 & 4 & 5 \\ 
\hline 
${\alpha}_1$
{% for a1 in ANGLE_A1_VERT -%}
&%% a1.angle %%$^{\circ}$%% a1.minus %%'
{%- endfor %}
\\
\hline 
${\beta}_1$ 
{% for a1 in ANGLE_B1_VERT -%}
&%% a1.angle%%$^{\circ}$%% a1.minus %%'
{%- endfor %}
\\ 
\hline 
${\alpha}_2$
{% for a1 in ANGLE_A2_VERT -%}
&%% a1.angle %%$^{\circ}$%% a1.minus %%'
{%- endfor %}
\\ 
\hline 
${\beta}_2$ 
{% for a1 in ANGLE_B2_VERT -%}
&%% a1.angle %%$^{\circ}$%% a1.minus %%'
{%- endfor %}
\\ 
\hline 
${\theta}$ 
{% for a1 in ANGLE_THETA -%}
&%% a1.angle %%$^{\circ}$%% a1.minus %%'
{%- endfor %}
\\ 
\hline 
$A$
{% for a1 in ANGLE_A -%}
&%% a1.angle %%$^{\circ}$%% a1.minus %%'
{%- endfor %}
\\ 
\hline 
\end{tabular}
\vspace{10pt}

其中$\theta$ = $\displaystyle\frac{1}{2}[({\alpha}_2-{\alpha_1})+({\beta}_2-{\beta}_1)]$，$A=\displaystyle\frac{1}{2}{\theta}$

\end{center}

\subsubsection*{(2)不确定度的计算}

$$\bar{A} =\frac{1}{5}\sum\limits_{i=1}^{5}{A_i}=%% AVERAGE_A %%rad$$
A类误差：$$u_a({\theta})=\sqrt{\displaystyle\frac{\sum\limits_{i=1}^{5} ({\theta}_i-\bar{\theta})^2}{5{\times}(5-1)}}=%% UA_THETA %% $$
B类误差：$$u_b({\theta})=\displaystyle\frac{\bigtriangleup\text{仪}}{\sqrt{3}}
= \frac{1'}{\sqrt{3}} = \frac{\pi}{180\times60\times\sqrt{3}} = 1.6794 \times 10^{-4} $$
${\theta}$不确定度：$$u({\theta})=\sqrt{{u_a({\theta})}^2+{u_b({\theta})}^2}=\sqrt{ %% UA_THETA %%^2 + 0.00016794^2} = %% U_THETA %% $$
A的不确定度：
$$u(A)=\displaystyle\frac{1}{2}u({\theta})=\displaystyle\frac{1}{2}{\times}%% U_THETA %% = %% U_A %% $$
相对不确定度：$$\displaystyle\frac{u(A)}{A}=%% RE_U %%$$
最终结果为：$$A{\pm}u(A) = %% RESULT_A %% {\pm} %% RESULT_UA %%rad$$